Analytic derivatives and the computation of GARCH estimates

In the context of univariate GARCH models we show how analytic first and second derivatives of the log-likelihood can be successfully employed for estimation purposes. Maximum likelihood GARCH estimation usually relies on the numerical approximation to the log-likelihood derivatives, on the grounds that an exact analytic differentiation is much too burdensome. We argue that this is not the case and that the computational benefit of using the analytic derivatives (first and second) may be substantial. Furthermore, we make a comparison of various gradient algorithms that are used for the maximization of the GARCH Gaussian likelihood. We suggest the implementation of a globally efficient computation algorithm that is obtained by suitably combining the use of the estimated information matrix with that of the exact Hessian during the maximization process. As this would appear a straightforward extension, we then study the finite sample performance of the exact Hessian and its approximations (that is, the estimated information, outer products and misspecification robust matrices) in inference.     

Assessment of meaningful change in routine outcome measurement (ROM) with a combination of a longitudinal and a ‘classify and count’ approach

To assess significant changes of health status in people receiving health care, distribution-based and anchor-based methods have been proposed. However, there is no real consensus on what method is the best for evaluating clinically meaningful change. To maximize the internal and external validity of outcome assessment, we propose combining two approaches as recommended by recent practical guidelines on this field. Specifically, we suggest applying longitudinal hierarchical linear models on subgroups of patients showing reliable change and reliable and clinically significant change. This combined approach improved the model’s ability (1) to quantify the magnitude of changes to be reliable and clinically meaningful and (2) to select significant predictors of changes. An empirical application on a prevalence sample of Italian outpatients attending four community mental health services was done. A cross-sectional model and three longitudinal models were applied on the entire study sample and reliable and clinically meaningful change subsamples to investigate the magnitude of change and the predictive effect on outcomes of clinical, socio-demographic and process variables on different patients’ subgroups. Differences were found suggesting that both the statistical method and the sample used to calculate individual changes affect the estimates. The main conclusion is that ignoring the longitudinal data structure or including patients with unreliable change at the follow-up might result in misleading inferences that can alter the real magnitude of changes and the contributions of predictors. The approach proposed provides robust feedback to clinicians on clinically significant change and can be recommended in outcome studies and research.     

Financial Liberalization, Property Rights, and Growth in an Overlapping-Generations Model

Using an endogenous growth model in which countries differ with respect to property rights protection, the paper analyzes the growth and welfare effects of removing capital controls, and studies the political support for a reform which improves the quality of property rights. When these are poorly protected, liberalization of capital movements may foster growth in the short run but eliminates it in the long run. The removal of capital controls may benefit agents at the time of liberalization, hurting future generations. Ceteris paribus , political support for a reform of property rights is stronger in the closed than in the open economy.     

Is training more frequent when the wage premium is smaller? Evidence from the European Community Household Panel

According to Becker [Becker, G., 1964, Human Capital, NBER, New York], when labour markets are perfectly competitive, general training is paid by the worker, who reaps all the benefits from the investment. Therefore, ceteris paribus, the greater the training wage premium, the greater the investment in general training. Using data from the European Community Household Panel, we compute a proxy of the training wage premium in clusters of homogeneous workers and find that smaller premia induce greater incidence of off-site training, which is likely to impart general skills. Our findings suggest that the Becker model provides insufficient guidance to understand empirical training patterns. Conversely, they are not inconsistent with theories of training in imperfectly competitive labour markets, in which firms may be willing to finance general training if the wage structure is compressed, that is, if the increase in productivity after training is greater than the increase in pay.     

Small Firm Investment and Financing Decisions: An Option Value Approach

This paper reviews and discusses recent developments undergone by investment theory, and tries to address both financial and real decisions within an uncertain environment, here, the Italian economy. According to the recent "option value" approach to investment, if differing degrees of reversibility characterize the accumulation process by groups of firms (small and larger firms), we should expect their investment decisions to differ under uncertainty. On the other hand, asset reversibility has an influence on firm financing policy, given the observed relationship between asset and liability composition. Assuming a different degree of investment reversibility for small and larger firms, we explore how they react to interest rate uncertainty using the Italian experience during the 1980s as a benchmark. The main result of this paper is that interest rate uncertainty exerts a negative influence on firms' investment demand. The relationship is stronger for large firms than for small firms. Another result is that firm leverage also shows a negative relationship with interest rate uncertainty.